Choice among lotteries when preferences are stochastic

Abstract: This paper discusses the problem of specifying probabilistic models for choices (strategies) with uncertain outcomes. The point of departure is an extension of the axiom system of the von Neumann-Morgenstern Expected utility theory to the case when the preferences are stochastic. This extended axiom system is combined with Luce Choice Axiom; "Independence from Irrelevant Alternatives", and imply a particular choice model that contains the Luce model as a special case. An additional invariance assumption is subsequently proposed that yields a complete characterization of the mathematical structure of the model. Keywords: Random tastes, choice among lotteries, random utility models, bounded rationality, probabilistic choice models, independence from irrelevant alternatives